488 



SCIENCE 



[JsT. S. Vol. XXXII. No. 823 



Ash Determinations and Ash Contents of Vege- 

 table Drugs: Edwaed Ivkemebs and W. H. 



ItENDALL. 



The Physiological Assay of the Heart Tonics of 

 the Digitalis Series: E. M. Houghtojt. 



Chables L. Paesons, 



Secretary 



SOCIETIES AND ACADEMIES 



THE AMERICAN MATHEMATICAL SOCIETY 



The seventeenth summer meeting of the society 

 was held at Columbia University on Tuesday and 

 Wednesday, September 6-7, 1910, extending 

 through two sessions on each day. Thirty-six 

 members were in attendance. Vice-president 

 Hutchinson occupied the chair. The council an- 

 nounced the election of the following persons to 

 membership in the society: Mr. F. S. Bartlett, 

 General Electric Company, Schenectady, N. Y. ; 

 Mr. R. D. Beetle, Dartmouth College; Professor 

 JST. C. Grimes, University of Arizona; Professor 

 E. T. H'Doubler, Miami University; Mr. Robert 

 Henderson, Equitable Life Assurance Society, New 

 York, N. Y.; Mr. G. F. McEwen, Stanford Uni- 

 versity; Professor Josephine A. Robinson, Berea 

 College. Ten applications for membership in the 

 society were received. 



On Tuesday evening twenty-five of the members 

 gathered at the usual informal dinner, always a 

 pleasant feature of the meetings. 



The following papers were read at the summer 

 meeting: 



L. E. Dickson : " On the factorization of integral 

 iunctions with p-adic coefiieients." 



L. E. Dickson: ''Determination of the binary 

 modular groups and their invariants." 



0. E. Glenn : " On the structure of p-ary forms." 



R. D. Carmichael : " Linear difference equations 

 and their analytic solutions." 



H. T. Burgess : " The simultaneous reduction of 

 a quadratic and a bilinear form by the same 

 transformation on both x's and y's." 



A. B. Coble : " On the reduction of the sextic 

 equation to the Valentiner form problem." 



Virgil Snyder : " The involutorial transforma- 

 tion of the plane, of order 17." 



L. E. Dickson: "An invariantive investigation 

 of irreducible binary forms." 



Arthur Ranum : " On the classification of sys- 

 tems of linear equations." 



Arthur Ranum: "The osculating sphere of a 

 developable surface." 



Peter Field : " The theory of degenerate rational 

 plane curves." 



J. E. Rowe : " Important covariant curves and 

 a complete system of invariants of the rational 

 quartic curve." 



G. D. Birkhoff: " General theory of linear dif- 

 ference equations." 



L. E. Dickson : " A fundamental system of in- 

 variants of the general modular linear group on 

 ■m variables. ' 



S. E. Slocum : " A general formula for the 

 shearing deflection of beams of arbitrary cross 

 section, either variable or constant." 



G. A. Miller : " Note on the solution of a system 

 of linear equations." 



G. A. Miller : " Some relations between substi- 

 tution group properties and abstract groups." 



Jacob Westlund: "On the relative discriminant 

 of a certain Kummer field." 



J. W. Bradshaw : " On a method of deriving 

 infinite products from certain infinite series." 



Anna J. Pell : " Infinite systems of linear equa- 

 tions with unsymmetrie systems of coelficients." 



Edward Kasner : " Conformal invariants of 

 cui-vilinear angles." 



Florian Cajori: "Fourier's improvement of the 

 Newton-Raphson method of approximation antici- 

 pated by Mourraille." 



Louis Ingold : " Note on identities connecting 

 certain integrals." 



E. 0. Lovett: "Generalizations of certain the- 

 orems concerning cases of collisions in the general 

 problem of several bodies." 



John Eiesland : " On minimal lines and surfaces 

 in four-dimensional space." 



John Eiesland : " Lie's line-sphere geometry 

 from the standpoint of four-dimensional space." 



E. D. Roe, Jr.: "A generalized definition of 

 limit." 



E. D. Roe, Jr. : " A new invariant function." 



H. H. Mitchell : " The subgroups of the hyper- 

 orthogonal group H0(3, p2^)." 



H. Beck : " Ein Seitenstiick zur Moebius'schen 

 Geometric der Kreisverwandtschaften." 



Abstracts of the papers will appear in the 

 November number of the Bulletin, 



The San Francisco section of the society met 

 at the University of California on Saturday, 

 September 24. The next regular meeting of the 

 society occurs on October 29. The winter meeting 

 of the Chicago section will be held at Minneapolis 

 with the American Association. 



F. N. Cole, 

 Secretary 



